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Polyacrilonitrile (PAN) is the main class of raw materials for the preparation of precursors for high-tensile carbon fibers. In this report we present our results of the computer simulations on the influence of the air-gap, the precipitation bath composition (the ratio of dimethyl sulfoxide/water), temperature and the amount of multiwall carbon nanotubes (MWCNT) on the internal structure of PAN-based precursor fibers. We have used coarse-grained models based on the time-dependent density functional theory (TDDFT) as well as the dissipative particle dynamics (DPD). The combination of both TDDFT and DPD methods allows us to study the internal structure formation of precursor fibers at different stages of dry-jet wet spinning method. We have performed a mapping of atomistic structures of PAN, dimethyl sulfoxide (DMSO), water and MWCNT on the corresponding coarse-grained representations. The models of dope solution jets with different thickness of the surface cuticle (which is formed when the jet passes through the air gap) have been used as the initial states in the simulations of the coagulation process inside the precipitation bath. Obtained results clearly show that the distribution of MWCNT in precursor fibers becomes homogeneous with increasing of water content in the precipitation bath composition. At the same time, the increase of water content causes the increasing of the number of nuclei of crystalline phase in the polymer matrix. Acknowledgements. We thank the Supercomputer center of Moscow State University for providing computer time on ”Lomonosov” supercomputer.